The sixth seed was playing in the last eight at Roland Garros for the third time in four seasons but had twice previously fallen at this stage.
Some inconsistent early serving aside, another slip-up never appeared likely as Zverev secured swift progress on Court Philippe-Chatrier.
Next is the winner of Daniil Medvedev versus Stefanos Tsitsipas, the other quarter-final in the bottom half of the draw that should prove rather more testing for the victor.
A peculiar first set saw only four games stay on serve as both players showed signs of frustration, first with Zverev offering an incredulous response to a tight but correct line call that allowed his opponent to hold.
Zverev's anger was short-lived, though, as error-strewn serving on both sides of the net ensured regular opportunities.
Davidovich Fokina inadvertently threw his racket into the stands after sending a deep forehand wide and another poor shot into the net sealed the opener for Zverev, who seized on the Spaniard's sloppy play once more to lead early in the second.
This was not an advantage he would cede, racing through the set in only 26 minutes as a tiring Davidovich Fokina won a meagre 11 points.
The struggling underdog saved two break points at the start of the third but then went long to tee up another opportunity that was duly taken, quickly bringing the finish line into view for Zverev.
Indeed, just 21 minutes were required this time to see out the match as Zverev's power made light work of the 22-year-old with two more ruthless breaks.